Many receivers are designed to detect signals with a pilot symbol. The pilot symbol may be one or more repetitions of a known data sequence or a pseudo-noise sequence. Detection of a pilot symbol indicates the presence of a data packet and also is used to determine the start of packet timing.
Orthogonal frequency division multiplexing (OFDM) has become the physical layer of choice for many wireless communications systems. Current wireless local area network (WLAN) and wireless metropolitan area network (WMAN) standards employ pilot symbols to aid detection and synchronization in the OFDM receiver. OFDM previously has been reported to be particularly sensitive to errors due to imperfect synchronization.
Pilot symbol assisted detection synchronization for OFDM relies on repeated pseudo-random binary sequences (PRBSs) being embedded in the pilot symbols, which are designed to have near-optimal unity peak to average power ratios (PAPRs) in both the time and frequency domain. Common approaches to pilot symbol assisted detection (and time offset estimation) are based on the correlation properties of the repeated PRBS in the pilot symbol. Similarly, the common approach to pilot symbol assisted synchronization (carrier frequency offset estimation) is based on exploiting the property that any frequency shift is common to the repeated PRBSs.
The susceptibility of pilot symbol assisted receivers to narrowband interference, with particular regard to OFDM systems is of particular importance as both WLAN and WMAN systems currently operate in unlicensed spectrum and therefore must co-exist with other unlicensed systems including cordless telephones, garage door openers, baby monitors and microwave ovens. All of these devices produce narrowband interference. Further, radio non-idealities such as transmitter carrier feedthrough (also known as carrier leakage) also introduce narrowband interference in the form of single-tone carrier residues. Previous work has proposed interference suppression using pre-coding. As well as this post-detection receiver techniques involving equalizers to improve bit error rate performance have been proposed.
A common model for a received, baseband (low pass equivalent) OFDM symbol, sampled with period T, isrn=as(nT−τS)e−j[2πν(nT−τS)+θ]+η(nT),  (1)where a is the flat fading channel amplitude, s(t) is the transmitted signal, n is the sample index, τS, ν and θ are the time-, frequency- and phase-offsets between transmitter and receiver introduced by a combination of system non-idealities and channel distortions, and η is complex additive white Gaussian noise (AWGN) having variance σw2. This model requires a number of assumptions including that the multipath channel is frequency non-selective (flat) and that the multipath channel is non time-varying (static). As the focus is on pilot symbol detection and frequency offset estimation, which are insensitive to sub-sample timing, the simplification τS=0 is made here without loss of generality.
Consideration of narrowband interference using this model producesrn=as(nT)e−j[2πνnT+θ]+be−j[2πξnT+φ]+η(nT),  (2)where b, ξ and φ are, respectively, the amplitude, frequency and phase of the demodulated narrowband interferer. Carrier feedthrough in the transmitter produces an in-band interferer at a frequency equal to the frequency difference between transmitter and receiver local oscillators which, depending on the amount of Doppler shift, will be equal or close to the signal frequency offset ν. Typically, the maximum carrier frequency offset is much less than the OFDM sub-carrier spacing and the pilot symbol is designed specifically to be able to resolve this frequency without ambiguity. Any DC offset will occur at ξ=0 and interference from other users of license-free spectrum may occur either singly (e.g. garage door openers, baby monitors, microwave ovens) or in pairs (e.g. cordless telephones) at any in-band frequency.
Pilot symbols for OFDM WLAN and WMAN standards comprise at least two repeated PRBSs, where each PRBS is of length L samples. While different receiver techniques are required for pilot symbol assisted detection and synchronization, depending on the number of PRBSs (including combinations of short and long PRBSs), all algorithms are based on the correlation properties between the repeated sequences. Alternatively if the pilot symbol contains a sequence known by the receiver, the algorithms can be based on the correlation properties between the pilot symbol and known sequence.
The lth output sample of an L-length sliding window integrate-and-dump cross-correlator of the received signal isPl=rlHrl+L,  (3)where r≐[r1, rl+1, . . . , rl+L−1]T and [.]H denotes Hermitian transpose. For a packet consisting of a pilot symbol preceded (l<0) and followed (l>2L−1) by noise only, analyses of the output of the correlator, Pl, in an interference-free environment show that |Pl| rises steeply to a peak (at l=0) before falling steeply to the noise-only level. Further, normalising |Pl| produces the non-central correlation coefficient
                                                                    ρ              l                                            ≐                                                                  P                l                                                                                                    R                  l                                ⁢                                  R                                      l                    +                    L                                                                                      ⁢                                  ⁢        where                            (        4        )                                          R          l                ≐                              r            l            H                    ⁢                      r            l                                              (        5        )            and the range of |ρl| is constrained to [0 1]. The receiver will declare a pilot symbol detection at the point where some threshold of correlation, TC, is exceeded, that is when|ρl|>TC.  (6)
Detection becomes more complicated where pilot symbols comprise more than two PRBSs, include a cyclic prefix (guard interval) and apply matched filter techniques to increase timing resolution and minimise false detection probability. However, the comparison specified by equation (6) is fundamental in every case.
In an environment with a narrowband interferer substitution of equation (2) into equation (3) yields
                                                        P              l                        =                                                            La                  2                                ⁢                                  S                  2                                ⁢                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    vLT                                                              +                                                Lb                  2                                ⁢                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    ξ                    ⁢                                                                                  ⁢                    LT                                                              +                              LaSb                ⁡                                  [                                                                                    ⅇ                                                                              -                            j                                                    ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                          vLT                                                                    ⁢                                                                        Ξ                          l                                                ⁡                                                  (                                                      v                            -                            ξ                                                    )                                                                                      +                                                                  ⅇ                                                                              -                            j                                                    ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                          ξ                          ⁢                                                                                                          ⁢                          LT                                                                    ⁢                                                                        Ξ                          l                          *                                                ⁡                                                  (                                                      v                            -                            ξ                                                    )                                                                                                      ]                                            +                                                η                  l                  H                                ⁡                                  (                                                            as                                              l                        +                        L                                                              +                                          b                      ⁢                                                                                          ⁢                                              ξ                                                  l                          +                          L                                                                                                      )                                            +                                                (                                                            a                      ⁢                                                                                          ⁢                                              s                        l                        H                                                              +                                          b                      ⁢                                                                                          ⁢                                              ξ                        l                        H                                                                              )                                ⁢                                  η                                      l                    +                    L                                                              +                                                η                  l                  H                                ⁢                                  η                                      l                    +                    L                                                                                ,                                          ⁢                                          ⁢          where                ⁢                                  ⁢                                  ⁢                                            Ξ              l                        ⁡                          (              x              )                                ≐                                    ⅇ                              -                                  j                  ⁡                                      [                                                                  2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        xlT                                            +                      θ                      -                      ϕ                                        ]                                                                        ⁢                          Φ              ⁡                              (                x                )                                                    ⁢                                  ⁢                                  ⁢        for        ⁢                                  ⁢                                  ⁢                                            Φ              ⁡                              (                x                )                                      ≐                                          1                SL                            ⁢                                                ∑                                      m                    =                    0                                                        L                    -                    1                                                  ⁢                                                      s                                          l                      +                      m                                                        ⁢                                      ⅇ                                                                  -                        j                                            ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      xmT                                                                                                    ,                                          ⁢                                          ⁢                                    s              l                        ≐                                                            ⅇ                                      -                                          j                      ⁡                                              [                                                                              2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                            viT                                                    +                          θ                                                ]                                                                                            ⁡                                  [                                                            s                      l                                        ,                                                                  s                                                  l                          +                          1                                                                    ⁢                                              ⅇ                                                                              -                            j                                                    ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                          vT                                                                                      ,                    …                    ,                                                                  s                                                  1                          +                          L                          -                          1                                                                    ⁢                                              ⅇ                                                                              -                            j                                                    ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      v                            ⁡                                                          (                                                              L                                -                                1                                                            )                                                                                ⁢                          T                                                                                                      ]                                            T                                ,                                          ⁢                                          ⁢                                    ξ              l                        ≐                                                            ⅇ                                      -                                          j                      ⁡                                              [                                                                              2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                            ξ                            ⁢                                                                                                                  ⁢                            T                                                    +                          ϕ                                                ]                                                                                            ⁡                                  [                                      1                    ,                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        ξT                                                              ,                    …                    ⁢                                                                                  ,                                          ⅇ                                                                        -                          j                                                ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  ξ                          ⁡                                                      (                                                          L                              -                              1                                                        )                                                                          ⁢                        T                                                                              ]                                            T                                                          (        7        )            and S is the mean magnitude of the PRBS. Similarly, insertion of equation (2) into equation (5) yields
                              R          l                =                                            La              2                        ⁢                          S              2                                +                      Lb            2                    +                      LaSb            ⁡                          [                                                                    Ξ                    l                                    ⁡                                      (                                          v                      -                      ξ                                        )                                                  +                                                      Ξ                    l                    *                                    ⁡                                      (                                          v                      -                      ξ                                        )                                                              ]                                +                                    η              l              H                        ⁡                          (                                                as                  l                                +                                  b                  ⁢                                                                          ⁢                                      ξ                    l                                                              )                                +                                    (                                                as                  l                  H                                +                                  b                  ⁢                                                                          ⁢                                      ξ                    l                    H                                                              )                        ⁢                          η              l                                +                                    η              l              H                        ⁢                                          η                l                            .                                                          (        8        )            
In the absence of signal, that is, in a narrowband interferer plus noise only environment, the probability of false pilot symbol detection may be evaluated as follows: Simplification of equation (7) and equation (8) leads to the approximations
                                          P            l                    ≈                                                                      Lb                  2                                ⁢                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    ξ                    ⁢                                                                                  ⁢                    LT                                                                              ︸                                  interference                  ⁢                                                                          ⁢                  term                                                      +                                                                                L                    ⁡                                          (                                                                        2                          ⁢                                                      b                            2                                                                          +                                                  σ                          w                          2                                                                    )                                                                      ⁢                                  η                  l                                                            ︸                                  composite                  ⁢                                                                          ⁢                  noise                  ⁢                                                                          ⁢                  term                                                                    ,                                  ⁢        and                            (        9        )                                                      R            l                    ≈                                                    L                ⁡                                  (                                                            b                      2                                        +                                          2                      ⁢                                              σ                        w                        2                                                                              )                                                            ︸                                  interference                  ⁢                                                                          ⁢                  term                                                      +                                          2                ⁢                                                      L                    ⁡                                          (                                                                        b                          2                                                +                                                  σ                          w                          2                                                                    )                                                                      ⁢                Re                ⁢                                                                  ⁢                                  {                                      η                    l                                    }                                                            ︸                                  composite                  ⁢                                                                          ⁢                  noise                  ⁢                                                                          ⁢                  term                                                                    ,                            (        10        )            respectively, where ηl is a zero mean complex Gaussian random variable with variance σw2. Details of the approximations may be inferred by reference to A. J. Coulson, “Maximum Likelihood Synchronization for OFDM Using a Pilot Symbol: Algorithms”, IEEE J. Selected Areas in Communications, vol. 19, no. 12, pp 2486-2494, December 2001.
Evaluation of the false detection probability p(|ρl|>TC)≡p(|Pl|2−TC2Rl2>0) in a narrowband interference-only environment may be found by comparison with expressions found in A. J. Coulson, “Maximum Likelihood Synchronization for OFDM Using a Pilot Symbol: Analysis”, IEEE J. Selected Areas in Communications, vol. 19, no. 12, pp 2495-2503, December 2001. It is sufficient for the purposes here to examine
                                                                        〈                                                                        ρ                    l                                                                    〉                            =                                                〈                                                                                P                      l                                                                            〉                                                  〈                                                                                    R                        l                                            ⁢                                              R                                                  l                          +                          L                                                                                                      〉                                                                                                                        =                                                                                                                              Γ                          2                                                +                                                  1                          /                                                      L                            ⁡                                                          (                                                                                                2                                  ⁢                                                                                                                                          ⁢                                  Γ                                                                +                                1                                                            )                                                                                                                                                                                                        (                                                          Γ                              +                              1                                                        )                                                    2                                                +                                                  1                          /                                                      L                            ⁡                                                          (                                                                                                2                                  ⁢                                                                                                                                          ⁢                                  Γ                                                                +                                1                                                            )                                                                                                                                                            ≈                                      Γ                                          Γ                      +                      1                                                                                  ,                                                          (        11        )            where <.> denotes the expected value, Γ≐b2/2σw2 is the interference to noise ratio, and noting that equation (11) is independent of the output of the cross-correlator l since both the magnitude of the narrowband interferer and the statistics of AWGN (additive white Gaussian noise) are time-invariant. The approximation is accurate for large values of L and for Γ0.
From equation (11) it is clear that the non-central correlation coefficient |ρl| will approach any practical value of TC, even at modest levels of interference. For example, the commonly-used value of TC2=0.8 will be exceeded, on average, by a narrowband interferer only 9 dB above the receiver noise floor. This means that a narrowband interferer will “swamp” a correlation-based detector based on equation (6), making it difficult to distinguish between the interference-only signal and an incoming pilot symbol, even though the pilot symbol may be tens of decibels greater in power than the interferer. More robust detection techniques, for example using a two-stage process employing a matched filter also will fail as a reasonably accurate forward estimate of frequency offset is required to produce the matched filter.
Frequency offset estimation is based on evaluating arg (Pl). Frequency offset estimation in the presence of narrowband interference but absence of signal will produce only an estimate of the carrier frequency of the interferer, which win be aliased if the carrier frequency is greater than the pilot symbol PRBS period inverse. In the presence of both signal and interference, the frequency offset estimate has an expected value of
                                                                        〈                                  v                  ^                                〉                            ≐                            ⁢                                                1                                      2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    LT                                                  ⁢                                  〈                                      arg                    ⁡                                          (                                              P                        0                                            )                                                        〉                                                                                                        =                            ⁢                                                1                                      2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    LT                                                  ⁢                                  〈                                      arg                    (                                                                                            La                          2                                                ⁢                                                  S                          2                                                ⁢                                                  ⅇ                                                                                    -                              j                                                        ⁢                                                                                                                  ⁢                            2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                            vLT                                                                                              +                                                                        Lb                          2                                                ⁢                                                  ⅇ                                                                                    -                              j                                                        ⁢                                                                                                                  ⁢                            2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                            ξ                            ⁢                                                                                                                  ⁢                            LT                                                                                              +                                                                                                                                                                              ⁢                                  LaSb                  ⁡                                      [                                                                                            ⅇ                                                                                    -                              j                                                        ⁢                                                                                                                  ⁢                            2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                            vLT                                                                          ⁢                                                                              Ξ                            l                                                    ⁡                                                      (                                                          v                              -                              ξ                                                        )                                                                                              +                                                                        ⅇ                                                                                    -                              j                                                        ⁢                                                                                                                  ⁢                            2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                            ξ                            ⁢                                                                                                                  ⁢                            LT                                                                          ⁢                                                                              Ξ                            l                            *                                                    ⁡                                                      (                                                          v                              -                              ξ                                                        )                                                                                                                ]                                                  )                            ⁢                                                                                      l                    =                    0                                                  〉                                                                        (        12        )            
After some manipulations, the frequency offset estimation bias can be shown to have an expected value of
                                                                        ϕ                bias                            ≐                            ⁢                                                〈                                      v                    ^                                    〉                                -                v                                                                                        =                            ⁢                                                1                                      2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    LT                                                  ⁢                a                ⁢                                                                  ⁢                                  tan                  ⁢                                    (                                                                                                                                                                        sin                              ⁡                                                              [                                                                  2                                  ⁢                                                                                                                                          ⁢                                                                      π                                    ⁡                                                                          (                                                                              v                                        -                                        ξ                                                                            )                                                                                                        ⁢                                  LT                                                                ]                                                                                      +                                                                                                                                                                                                          2                              l                                                        ⁢                            XY                            ⁢                                                                                                                  ⁢                                                          sin                              ⁡                                                              [                                                                                                      π                                    ⁡                                                                          (                                                                              v                                        -                                        ξ                                                                            )                                                                                                        ⁢                                  LT                                                                ]                                                                                                                                                                                                                                                                                                            l                              2                                                        +                                                          cos                              ⁡                                                              [                                                                  2                                  ⁢                                                                                                                                          ⁢                                                                      π                                    ⁡                                                                          (                                                                              v                                        -                                        ξ                                                                            )                                                                                                        ⁢                                  LT                                                                ]                                                                                      +                                                                                                                                                                                                          2                              l                                                        ⁢                            XY                            ⁢                                                                                                                  ⁢                                                          cos                              ⁡                                                              [                                                                                                      π                                    ⁡                                                                          (                                                                              v                                        -                                        ξ                                                                            )                                                                                                        ⁢                                  LT                                                                ]                                                                                                                                                                                          )                                                                                        (        13        )            where ι≐aS/b is the signal-to-interferer ratio, X≐|Φ(ν−ξ)|, χ≐arg(Φ(ν−ξ)) and Y≐ cos [θ−φ+χ+π(ν−ξ)LT].
Clearly, the value of this bias significantly depends on the difference between the pilot symbol frequency offset and the interferer carrier frequency (ν−ξ), the signal-to-interferer ratio, ι, and the properties of the PRBS, manifested through Φ(ν−ξ). Of primary importance is that the bias depends on the difference ν−ξ, rather than the frequency offset, ν, itself. Thus, for an interferer having a large carrier frequency ξ, the estimation bias φbias can significantly exceed ν itself even for a large signal-to-interference ratio, as illustrated in FIG. 1.
An alternative “detection metric” to that of equation (4) has been proposed. This is the central correlation coefficient
                                                                    ρ              l              ′                                            ≐                                                                  P                l                ′                                                                                                    R                  l                  ′                                ⁢                                  R                                      l                    +                    L                                    ′                                                                    ⁢                                  ⁢        where                            (        14        )                                                                                                      P                  l                  ′                                ≐                                ⁢                                                      (                                                                  r                        l                        H                                            -                                                                        r                          _                                                l                        *                                                              )                                    ⁢                                      (                                                                  r                                                  l                          +                          L                                                                    -                                                                        r                          _                                                                          l                          +                          L                                                                                      )                                                                                                                          =                                ⁢                                                                            r                      l                      H                                        ⁢                                          r                                              l                        +                        L                                                                              -                                      L                    ⁢                                                                  r                        _                                            l                      *                                        ⁢                                                                  r                        _                                                                    l                        +                        L                                                                                                                                ⁢                                  ⁢                              for            ⁢                                                  ⁢                                          r                _                            l                                ≐                                    1              L                        ⁢                                          ∑                                  m                  =                  0                                                  L                  -                  1                                            ⁢                              r                                  l                  +                  m                                                                    ⁢                                  ⁢        and                            (        15        )                                          R          l          ′                ≐                                            r              l              H                        ⁢                          r              l                                -                      L            ⁢                                          r                _                            l              *                        ⁢                                          r                _                            l                                                          (        16        )            noting that, in contrast with normal practice, •′ is used here to denote central moments and central random variables to maintain consistency with previously used notation. Intuitively, it is expected that the central correlation “detection metric” of equation (14) is more robust than the traditional non-central correlation coefficient of equation (4) in the presence of a near DC narrowband interferer.
In a narrowband interference-only environment, by inserting equations (7) and (8) into equations (15) and (16), and then into equation (14), the expected value of |ρl′| can be shown to be
                                                                        〈                                                                        ρ                    l                    ′                                                                    〉                            ⁢                                                          =                                                          ⁢                                                〈                                                                                P                      l                      ′                                                                            〉                                                  〈                                                                                    R                        l                        ′                                            ⁢                                                                                          ⁢                                              R                                                  l                          +                          L                                                ′                                                                              〉                                                                                                                                                                                    =                                                                                                            ⁢                                                                                                                                                      Γ                              ~                                                        2                                                    ⁢                                                                                                          +                                                                                                          ⁢                                                      1                            /                                                          L                              ⁡                                                              (                                                                                                      2                                    ⁢                                                                                                                                                  ⁢                                                                          Γ                                      ~                                                                                                        ⁢                                                                                                                                          +                                                                                                                                          ⁢                                  1                                                                )                                                                                                                                                                                                                        (                                                                                                Γ                                  ~                                                                ⁢                                                                                                                                  +                                                                                                                                  ⁢                                1                                                            )                                                        2                                                    ⁢                                                                                                          +                                                                                                          ⁢                                                      1                            /                                                          L                              ⁡                                                              (                                                                                                      2                                    ⁢                                                                                                                                                  ⁢                                                                          Γ                                      ~                                                                                                        ⁢                                                                                                                                          +                                                                                                                                          ⁢                                  1                                                                )                                                                                                                                                                                          ⁢                                                                          ≈                                                                          ⁢                                                            Γ                      ~                                                                                      Γ                        ~                                            ⁢                                                                                          +                                                                                          ⁢                      1                                                                      ,                            ⁢                                                                                                      (        17        )            where {circumflex over (Γ)}≐(1−|Ψ(ξ)|2)b2/2σw2 is the modified interference to noise ratio for
            Ψ      ⁡              (        ξ        )              ≐                  ⅇ                  j          ⁢                                          ⁢          π          ⁢                                          ⁢                      ξ            ⁡                          (                              L                -                1                            )                                ⁢          T                    ⁢                        sin          ⁢                                          ⁢          π          ⁢                                          ⁢          ξ          ⁢                                          ⁢          LT                          L          ⁢                                          ⁢          sin          ⁢                                          ⁢          π          ⁢                                          ⁢          ξ          ⁢                                          ⁢          T                      ,and the approximation is accurate for large values of L and for {circumflex over (Γ)}0. Note that, as with |ρl|, |ρl′| is independent of l in the absence of a signal.
The mean improvement in interference rejection gained through the use of |ρl′| over the use of |ρl| is shown in FIG. 2 as a function of the narrowband interferer carrier frequency ξ normalised to the OFDM sub-carrier spacing 1/(LT). Also shown on FIG. 2, for reference, are the frequency responses of high pass filters of increasing order and the maximum carrier frequency offset specified by the IEEE 802.11a standard.
This Figure shows, firstly, that the DC offset rejection gained through the use of equation (14) in place of equation (4) is substantial. Secondly, the frequency response of the improvement in narrowband interference rejection gained through the use of equation (14) in place of equation (4) is very similar to that of a first order filter with a cut-off (3 dB) frequency of about ½ξLT such as may be implemented, for example, using a coupling capacitor on the input to the analog-to-digital converter. Thirdly, the interference rejection at the maximum expected frequency offset for IEEE 802.11a is less than one decibel. IEEE Standard 802.11a-1999, Part 11: Wireless LAN Medium Access Control (MAC), and Physical Layer (PHY) Specifications—High-speed Physical Layer in the 5 GHz Band, 1999 is incorporated herein by reference. Referring to the IEEE 802.11a standard, for a maximum input signal level of −30 dBm (17.10.3.4) and a maximum carrier leakage of −15 dBr (17.3.9.6.1), the additional carrier leakage attenuation required at the receiver to suppress the maximum received carrier level below the minimum receiver sensitivity of −82 dBm (17.3.10.1) is 37 dB. From FIG. 2, a tenth order high pass filter does not provide this attenuation across the range of allowable carrier frequency offsets, which means that the only practical reliable method of preventing carrier leakage from producing false detection correlations is accurate time-gating at the transmitter.
Further, a receiver having a dynamic range of 50 dB must be able to suppress narrowband interferers at any in-band frequency by at least 50 dB to prevent false detection correlations. Clearly, the use of central correlation alone does not achieve this.
As described above neither the non-central correlation coefficient pi nor the central correlation coefficient ρl′ by themselves are sufficient to detect a pilot symbol in the presence of narrowband interference without additional processing.